EXCHANGE 


UNIVERSITY  OF  PENNSYLVANIA 


ION  ACTIVITY  IN  HOMOGENEOUS 

CATALYSIS 

THE  VELOCITY  OF  HYDROLYSIS  OF 
ETHYL  ACETATE 


BY 

ROBERT  PFANSTIEL 


A  THESIS 

PRESENTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  IN 

PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS  FOR 

THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 

IN  CHEMISTRY 


®t?r  (gollrgiatp  ilrpsja 

GEORGE  BANTA  PUBLISHING  COMPANY 

MENASHA,  WIS. 

1922 


UNIVERSITY  OF  PENNSYLVANIA 


ION  ACTIVITY  IN  HOMOGENEOUS 

CATALYSIS 

THE  VELOCITY  OF  HYDROLYSIS  OF 
ETHYL  ACETATE 


BY 

ROBERT  PFANSTIEL 

\\ 


A  THESIS 

PRESENTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  IN 

PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS  FOR 

THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 

IN  CHEMISTRY 


QHf*  OJoUrgiatr  fln-su 

GEORGE  BANTA  PUBLISHING  COMPANY 

MENASHA,  WIS. 

1922 


ACKNOWLEDGMENT 

This  work  was  undertaken  at  the  suggestion  of  Dr.  Herbert  S. 
Harned  to  whom  the  author  is  deeply  indebted  for  its  success. 


0 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 
THE  VELOCITY  OF  HYDROLYSIS  OF  ETHYL  ACETATE 

As  a  result  of  considerable  evidence,  Mac  Innes  (Jour.  Amer. 
Chem.  Soc.  41,  1086  [1919])  has  arrived  at  the  conclusion  that  in 
solutions  of  the  same  molality  of  hydrochloric  acid,  lithium,  sodium, 
and  potassium  chlorides,  the  chlorine  ion  has  the  same  activity. 
He  further  made  the  assumption  that  in  a  solution  of  a  given  strength, 
the  activities  of  the  potassium  and  chlorine  ions  are  the  same. 
These  hypotheses  received  considerable  confirmation  in  dilute  solu- 
tions from  the  electromotive  force  measurements  of  Ming  Chow 
(Jour.  Amer.  Chem.  Soc.  42,  477  [1920])  and  in  concentrated  solu- 
tions by  Harned  (Jour.  Amer.  Chem.  Soc.  42,  1808  [1920]).  On  the 
basis  of  these  assumptions,  Harned  calculated  from  existing  electro- 
motive force  data  the  individual  ion  activity  coefficients  of  these 
uni-univalent  electrolytes.  If  Mac  Innes'  assumptions  are  correct 
it  follows  from  these  calculations  that  the  activity  coefficient  of  the 
hydrogen  ion  in  dilute  solutions  of  hydrochloric  acid  decreases  until 
a  concentration  of  0.15  M.  is  reached  and  then  increases  quite 
rapidly.  In  any  event,  this  activity  coefficient  must  exhibit  a 
minimum  in  the  neighborhood  of  from  0.1  M.  to  0.2  M.  concentra- 
tion. 

These  conclusions,  if  true,  or  valid  within  narrow  limits,  will 
be  of  considerable  importance  in  the  calculation  of  equilibria  in 
solutions  as  well  as  homogeneous  catalysis.  Consequently,  this 
investigation  was  undertaken  with  the  purpose  of  finding  out  whe- 
ther further  support  for  the  above  hypothesis  could  be  obtained 
from  a  study  of  hydrogen  ion  catalysis. 

It  has  been  found  that  the  monomolecular  velocity  constant  of 
hydrolysis  of  ethyl  acetate  in  dilute  solutions  of  hydrochloric  acid  is 
roughly  proportional  to  the  concentration  of  the  acid.  It  was  first 
thought  that  the  velocity  of  hydrolysis  was  proportional  to  the 
hydrogen  ion  concentration,  but  it  was  soon  found  that  the  velocity 
constant  increased  with  increasing  acid  concentration  more  rapidly 
than  the  hydrogen  ion  concentrations  as  computed  from  the  con- 
ductance or  conductance  viscosity  ratios.  To  explain  this,  Senter 

1 


•2  ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 

(Trans.  Chem.  Soc.,  91,  467  [1907]),  Acree  (Amer.  Chem.  Jour., 
37,  410,  and  38,  258  [1907]),  Taylor  (Meddel.  K.  Vetensk.  Nobelinst., 
2,  No.  37  [1913]),  and  others  have  proposed  the  theory  that  the 
undissociated  acid  molecule,  as  well  as  the  hydrogen  ion,  exerts 
a  catalytic  effect.  In  contradistinction  to  this,  another  theory 
has  been  proposed  which  relates  the  reaction  velocity  to  the  ion  ac- 
tivities as  defined  by  G.  N.  Lewis  (Proc.  Amer.  Acad.  Arts  Sci.  43, 
259  [1907];  Jour.  Amer.  Chem.  Soc.,  35,  1  [1913],  etc.).  Lewis 
has  shown  that  in  a  chemical  equilibrium  the  exact  thermodynamic 
expression  for  the  law  of  mass  action  of  a  general  reaction  such  as 
aA+bB+  .  .  .  .±=>dD+eE+  ....  is 


*  =  -          ...............  .....  ..............  (1) 

ttj  •  4 

where  a^  aB)  etc.,  represent  the  activities  of  the  species  A,  B,  etc., 
respectively,  and  K  is  an  equilibrium  constant.  Thus,  if  the  equili- 
brium is  a  dynamic  one,  the  velocity  from  left  to  right  and  the 
velocity  from  right  to  left  will  be  given  respectively  by 


If  the  velocities  depend  on  successive  states  of  equilibria,  and  no 
interfering  factors  such  as  contact  surfaces,  light  radiation,  etc., 
are  present,  the  above  equations  for  the  velocities  are  a  thermo- 
dynamic necessity. 

At  the  present  time  the  mechanism  of  ester  hydrolysis  is  not  well 
known.  The  theory  which  has  the  most  evidence  in  its  favor  is  the 
one  which  assumes  the  formation  of  an  intermediate  compound 
(Stieglitz—  Congress  of  Arts  and  Sciences—  St.  Louis  4,  276  [1904]). 
Here  the  reaction  takes  place  in  two  steps.  The  first  is  a  rapid  reac- 
tion between  the  ester,  hydrogen  ion,  and  water,  to  form  the  inter- 
mediate compound,  and  the  second  is  a  slow  decomposition  of  the 
intermediate  compound  producing  the  alcohol  and  acid,  and  regen- 
erating the  hydrogen  ion.  Thus 

[-0-H  -|  + 

Vro-n 
CH3C   O  C2#5j  ........  (a) 

^ 

[-0-H  -I  + 

Vro-n 
CH3C   0  C2H<,]±=?CH3COOH+C2HbOH+H+  .......  (b) 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 

The  equilibrium  of  reaction  (a)  is  represented  by 


ae  •  oH  •  aw 

where  0;,  ae,  aE,  and  aw  are  the  activities  of  the  intermediate  com- 
pound, ester,  hydrogen  ion,  and  water  species.    The  velocity  of  the 
reaction  from  left  to  right  will  be  given  by 
»i  =  ka\ 

Hence  DI  =  ki  ae  -  0H  •  aw (3) 

Throughout  this  paper  ki  will  represent  the  velocity  from  left  to  right. 
Since  by  definition  Fe-c  equals  ae,  where  Fe  is  the  activity  co- 
efficient of  the  ester  and  c  is  its  concentration,  substitution  in  (3) 
gives 

Vi  =  ki(Fe'c)-aE-aw (4) 

At  a  given  temperature  ki  remains  constant  under  changing 
conditions  of  all  other  factors  in  equation  (4) 
Let  k\=ki  •  #H  '  #wj 

Then  — ^—  =ki (4a) 

#H  *  aw 

Substituting  the  value  of  k\,  in  (4)  gives 

0i  =  *Y(Fe-c) (4b) 

From  (4a),  k\  is  proportional  to  #H  and  aw.  During  the  course 
of  reaction  in  a  given  experiment  #H  and  aw  remain  constant  and 
k\  therefore  represents  the  velocity  constant  in  each  experiment. 
Since  the  velocity  constant  is  obtained  by  measurement  of  c,  equa- 
tion (4b)  shows  that  k\F6  instead  of  k\  is  obtained.  Therefore  in  the 
Tables  to  follow  k'iFe  will  always  represent  the  velocity  constant. 

k'iF 

Equation  (4a)  shows  that —  will  not  remain  constant  if  Fe  vary. 

#H  *  aw 

Fe  will  vary  if  the  solubility  of  the  ester  changes  with  changing 
hydrochloric  acid  concentration  because  Fe  is  a  function  of  the 
solubility.  This  can  be  seen  from  the  following  thermodynamic 
reasoning:  The  activity  of  the  ester  in  a  saturated  solution  in  the 
presence  of  the  liquid  ester  at  the  same  pressure  and  temperature 
will  always  have  the  same  value.  Therefore,  if  a',  a",  a'",  etc., 
represent  the  activities  of  the  ester  in  varying  acid  concentrations, 
and  C',  C",  C"'  etc.,  represent  the  concentrations  of  the  ester  in  the 
saturated  solutions, 

Thena'««"-a'"=etc. 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 


C 


or 
"      '" 


Substituting  6",  5",  5'",  etc.,  or  the  solubilities  for  the  conten- 
trations  in  the  saturated  solutions  gives 

Fe'S'  =  Fe"S"  =  Fe'"Sf"  =  FeS  =  constant  ............  (5) 

From  (4a)  and  (5)  is  obtained 

kl/  Fe   -  S  =  h  \F9  S)  =  constant  ...................  (Sa) 

flH'tfw 

Earlier  work  on  this  subject  is  not  sufficient  to  prove  the  validity 
of  equation  (5a).  A  compilation  of  previous  data  taken  from  the 
work  of  Taylor  (Meddel.  K.  Vetensk.  Nobelinst.,  2,  No.  37,  [1913]), 
Kay  (Proc.  Royal  Soc.  Edinb.,  22,  484  [1897])  and  Lunden  (Zeit. 
Phy.  Chem.,  49,  189  [1904])  on  the  hydrolysis  of  ethyl  acetate  and 
other  esters  is  contained  in  a  paper  by  Schreiner  (Zeit.  anorg.  chem., 
116,  102,  [1921]).  These  results  are  reproduced  in  Table  I. 

TABLE  I 

Ethyl  Acetate  Hydrolysis 

Hydrochloric  acid  Concentration  (k\  •  Fe)  •  106  (feV-flJ-lO8 


c  c 

0.010  2.93  293. 

0.025  6.99  280. 

0.050  13.83  278. 

0.100  28.29  283. 

0.132  38.10  288. 

0.150  43.20  288. 

0.200  57.00  285. 

0.250  71.60  286. 

0.479  138.00  288. 

0.493  145.00  296.    * 

Thus,  the  velocity  constant  divided  by  the  concentration  passes 
through  a  minimum  at  about  0.05  M.  hydrochloric  acid.  This  is 
similar  to  the  behavior  of  the  activity  coefficient  of  the  hydrogen  ion 
as  mentioned  above.  This  evidence  is  by  no  means  conclusive, 
but  is  suggestive  due  to  the  parallelism  between  these  properties. 
Consequently,  further  careful  work  has  been  undertaken  in  order  to 
clear  up,  if  possible,  some  of  the  difficulties. 

I.     EXPERIMENTAL 

The  experimental  method  employed  throughout  in  determining 
the  velocity  constants  is  the  same  as  that  usually  employed,  namely, 


I 

ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS  5 

titration  from  time  to  time  of'  the  total  acid  present  in  the  ester- 
hydrochloric  acid  mixture  by  means  of  sodium  and  barium  hydroxide 
solutions.  Densities  of  all  the  solutions  were  determined  so  that  the 
calculations  could  be  made  on  either  a  weight  or  a  volume  normal 
basis.  Further,  all  solutions  were  so  standardized  that  it  was  possible 
to  compute  the  absolute  quantities  of  all  the  molecular  species  pres- 
ent at  any  time  during  the  course  of  the  reaction.  Since  calcula- 
tions were  made  by  both  the  monomolecular  formula  and  by  the 
general  kinetic  formula  for  the  reaction,  it  will  be  necessary  to  discuss 
the  procedure  in  some  detail. 

(a)    MATERIALS 

Ethyl  acetate  was  prepared  from  alcohol  and  acetic  acid,  and 
purified  in  the  usual  way.  After  repeated  fractional  distillation, 
the  portion  which  passed  over  between  77°  and  78°  was  collected  for 
the  investigation.  Analysis  of  this  fraction  gave  98.81%  saponifiable 
ester,  free  from  acetic  acid.  Tests  for  free  acetic  acid  were  made 
from  time  to  time  during  the  course  of  the  investigation  and  in  no 
case  was  it  found  present. 

Constant  boiling  hydrochloric  acid  was  diluted  to  3M,  and  checked 
by  gravimetric  analysis.  All  solutions  of  the  acid  were  made  from 
this  sample  by  the  weight  method  and  were  correct  to  within  0.1% 
of  the  total  hydrochloric  acid  content.  Conductivity  water  freed 
from  carbon  dioxide  by  boiling  was  employed. 

The  sodium  hydroxide  and  barium  hydroxide  solutions  used  to 
titrate  the  total  acid  (hydrochloric,  and  acetic  formed  during  the 
hydrolysis  of  the  ester)  were  kept  in  carbon  dioxide  free  bottles. 
The  sodium  hydroxide  solutions  were  freed  from  carbonate  by  the 
addition  of  small  quantities  of  barium  hydroxide. 

All  flasks  used  were  cleaned  with  a  sulphuric-chromic  acid  mix- 
ture, followed  by  the  introduction  of  a  jet  of  steam.  After  drying, 
they  were  provided  with  paraffined  cork  stoppers. 

(b)    METHOD  OF  PROCEDURE 

Each  determination  was  carried  out  in  a  %  liter  flask.  In  all 
the  determinations  200  grams  of  water  were  employed.  The  molal 
concentration  of  the  hydrochloric  acid  (mols  of  hydrochloric  acid  in 
1000  grams  of  water)  varied  from  0.01  to  1.5.  In  a  given  series  the 
same  quantity  of  ethyl  acetate  was  added  to  each  flask.  Thus  in  every 
determination  of  a  given  series  the  same  quantity  of  water  and  the 


6  ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 

same  quantity  of  ester  was  employed,  the  only  variable  being  the 
hydrochloric  acid  content.  Two  series  of  results  were  obtained  using 
5  c.c.  and  1  c.c.  of  ester  to  100  grams  of  water. 

In  every  determination,  the  quantity  of  hydrochloric  acid  solu- 
tion necessary  for  a  given  molal  concentration  of  hydrochloric  acid 
in  200  grams  of  water  was  calculated,  and  then  weighed  in  a  small 
weighing  bottle,  care  being  taken  to  avoid  loss  by  evaporation  while 
weighing.  It  was  then  washed  into  a  previously  weighed  250  c.c. 
flask.  Water  was  then  added  until  the  weight  obtained  was  equal 
to  the  weight  of  the  flask,  the  HC1,  and  200  grams  of  water.  The 
flask  was  then  placed  in  a  thermostat  in  which  a  temperature  of 
25°  ±0.01  was  maintained.  After  the  contents  of  the  flask  had 
acquired  the  same  temperature  as  the  bath,  ethyl  acetate  at  25° 
was  added  to  the  solution  from  a  pipette.  Two  series  of  experiments 
were  conducted,  differing  from  one  another  only  in  the  ester  concen- 
tration. In  the  one  series  10  c.c.,  and  in  the  other  2  c.c.  of  ethyl 
acetate  were  added  to  each  solution.  In  each  case,  the  quantity  of 
ester  added  was  determined  by  taking  the  average  weight  of  several 
pipetted  portions  of  ethyl  acetate,  the  same  conditions  as  to  tem- 
perature and  delivery  of  pipette  being  observed. 

The  addition  of  as  much  as  10  c.c.  of  ester  caused  a  noticeable 
rise  in  temperature,  amounting  to  1°  in  cases  where  the  molal 
concentration  of  hydrochloric  acid  was  0.5  or  higher.  Therefore 
before  pipetting  for  the  initial  titration,  it  was  necessary  to  wait  until 
the  temperature  was  reduced  to  25°. 

As  soon  as  all  the  ester  was  dissolved  and  the  liquid  had  assumed 
the  temperature  of  the  bath,  a  10  c.c.  portion  was  withdrawn  with  a 
pipette  and  delivered  into  a  beaker  containing  a  little  water  and 
some  phenolphthalein.  While  the  pipette  was  delivering,  sodium 
hydroxide  from  a  burette  was  introduced  at  a  rate  sufficient  to 
neutralize  the  hydrochloric  acid  in  the  hydrolyzing  solution  as  fast 
as  it  was  discharged  from  the  pipette.  Since  the  time  of  the  initial 
titration  and  all  subsequent  titrations  were  noted  the  time  always 
taken  was  the  instant  when  the  pipette  was  half  discharged.  From 
eight  to  ten  titrations  were  made  in  each  determination  at  successive 
time  intervals  during  the  course  of  the  reaction.  A  0.04426  N.  barium 
hydroxide  solution  was  employed  in  all  cases  as  titrating  agent,  and 
for  solutions  containing  the  higher  hydrochloric  acid  concentrations 
a  stronger  solution  of  sodium  hydroxide  was  also  used.  In  the  latter 
case,  the  initial  titrations  were  made  with  the  stronger  alkali,  and 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS  7 

the  subsequent  titrations  were  'made  by  first  adding  the  same  amount 
of  sodium  hydroxide  as  was  used  in  the  initial  titration  and  then 
completing  the  determination  by  the  addition  of  barium  hydroxide. 

(c)    KINETICS  OF  THE  REACTION 

In  what  follows,  a  very  careful  study  has  been  made  of  the 
velocity  constants  calculated  by  both  the  simplified  and  approxi- 
mate monomolecular  reaction  equation,  and  the  more  general 
kinetic  equation  which  takes  into  consideration  the  reverse  reaction. 

(1)  The  Kinetics  of  the  First  Order  Reaction. 

The  general  equation  for  the  kinetics  of  the  reaction,  RCOOR'-}- 
H^O±^RCOOH-\-R'OHt  in  going  from  left  to  right  and  assuming 
that  the  activities  of  the  four  molecular  species  are  proportional  to 
their  concentrations  and  that  the  hydrogen  ion  activity  remains 
constant,  will  be 

dr 

£  =%"  (A-x)  (B-x)-kzx*  ...............  (6) 

at 

dx 

where  —  is  the  velocity,  A  and  B  the  initial  concentrations  of  ester 
dt 

and  water,  x  the  amount  of  ester  changed  in  the  time,  t,  and  ki"  and  k% 
are  the  velocity  constants  of  hydrolysis  and  esterification  respec- 
tively. Since  the  water  concentration,  B,  varies  only  slightly  during 
the  reaction,  and  since  the  reaction  goes  nearly  to  completion  when 
a  relatively  large  quantity  of  water  is  present,  equation  (6)  may  be 
reduced  to  the  simpler  and  approximate  monomolecular  equation 

^=ki"(A-X)  ....................  '  .......  (7) 

dt 

which  upon  integration  takes  the  well  known  form 


t       A  —  X 
This  equation  when  expressed  in  terms  of  the  titers  becomes 

kS'^ln7^^  ........................  (9) 

t     Toc-r 

where  T«>  is  a  number  slightly  greaterf  than  the  final  titer,  T0  the 
initial  titer,  and  T  the  titer  at  any  time  /. 

•k"-W*& 

t  Explained  later. 


8  ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 

(2)  The  General  Kinetic  Equation. 

In  equation  (6),  namely,  —  =  kl"  (A-x)  (B-x)-k2x2,  V  and  k* 

dt 

are  both  unknowns.    Therefore  kz  must  be  eliminated. 

Let    ^  =  0  =  *i"  (A-x)  (B-x)-kzx2, 
dt 

kz      (A—x)  (B  —  x)      r,  f       ....    .  .x 

then  —  = — =  K  (equilibrium  constant) 

ki"               x2 
and    k*  =  ki"-K  (10) 

K  can  be  determined  experimentally  since  —  =  0  represents  the 

dt 

end  point  in  a  titration. 

(Subst.  for  k*  in  [6])  -  =  £/'  (A-x)  (B-x)-^"  Kx2 (11) 

dt 

or  —  =  fc"  {x*-(A+B)x+AB}  -h"  Kx* 

dt 


or  —  =  RI     (I  —  A 

dt  '  \         1-K       1-K 

dx  =k1"  (l-K)dt..  ..(12) 


.     A+B    .A-B 

x2 x+ 


'1-K       1-K 

C..  ..(13) 


dx 

xZ_A±B      A^B 
1-K       1-K 


To  integrate  the  expression  on  the  left  hand  side  of  equation  (13), 
let 


and  a*    -4-f.  ........................  (15) 

1  —  K 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 

r dx — _=  r         dx 


Then  /    2__ 

J  X      l-K       l-K 


/dx  I          dx I  = 

J  J 

= In  (ft  —  x)—- In  (a  —  x)  = 

ft  —  a  ft  —  a 

1      .    ft  —  x  „,. 

= In (lo) 


—  a       a  — 


Equation  (13)  becomes  —  —  In^^=k1"  (l-k)t+C  .........  (17) 

ft—  a        a—x 

To  evaluate  the  constant  C,  let  t  =  o,  then  x  =  o,  and 


ft-  a       a 
Subst.  value  of  Cin  (17):     —  In  a(/3~^  =  ^"(l-ff)*  ........  (18) 


2.3026  atf-.) 

(1-X)  (|8-o)<        B  (a-*) 

For  substituting  back  in  equation  (19)  the  values  of  a  and  j3,  in 
terms  of  A,  B,  and  K,  equations  (14)  and  (15)  must  be  solved  simul- 
taneously. 

4A-B  (l-K) 


2  (l-K) 


A+B-V(A+B)*-4  A-B  (l-K) 
2  (l-K) 


2.3026  A+B-(A+B)*-4  AB(1~K) 


-4:  A-B  (l-K)          A+B+(A  +B)*-4  AB(l-K) 


-4  AB    l-K-2    l-K)x 


-4:  AB  (l-K)-2  (l-K)x 


10  ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 

Equation  (20)  is  reduced  to  a  simpler  form  by  letting 


2.3026  A+B-V(A+B)2-4A-B(1-K) 


V(A+B)2-4AB  (1-K)  A+B+V(A+B)*-4A'B(1-K) 

X  2  (l-K),  and  n  =  A+B-  V(A+B)*-4:  A-B  (1-K). 
By  substitution  in  (20) 


Griffith  and  W.  C.  McC.  Lewis,  (Jour.  Chem.  Soc.,  109,  67  [1916]) 
indicate  how  equation  (6)  may  be  integrated  by  a  different  substitu- 
tion. Knoblauch  (Zeit.  fur  Physk.  Chemie  22,  268,  [1897])  integrated 
a  similar  equation  by  a  different  substitution. 

(D)    CALCULATION,  AND  TABLES  OF  VELOCITY  CONSTANTS 
COMPUTED  FROM  MONOMOLECULAR  EQUATION 

In  computing  ki"  according  to  the  monomolecular  equation 
(9),  Too  represents  the  quantity  of  alkali  which  would  be  required 
for  titration  after  complete  hydrolysis.  Since  the  reaction  does  not 
go  to  completion,  T»  cannot  be  determined  experimentally.  There- 
fore rw  was  calculated  in  each  experiment  as  follows:  The  weight 
of  10  c.c.  of  the  solution,  delivered  from  the  pipette  used  in  each 
titration,  was  determined.  Let  this  be  "a."  In  the  preparation  of 
the  solutions  the  weight  of  each  component  was  known.  Let  b 
equal  the  weight  of  the  water,  d  the  weight  of  hydrochloric  acid,  and 

e  the  weight  of  the  ester  in  the  reaction  flask.     Then  -  •  d  is 

b+d+e 

the  number  of  grams  of  hydrochloric  acid,  and  -  •  e  is  the 


number  of  grams  of  ethyl  acetate  (assuming  no  hydrolysis),  in  each 
pipette.  Therefore,  the  alkali  equivalent  of  both  the  hydrochloric 
acid  and  the  ethyl  acetate  in  cubic  centimeters,  or  TM  is  readily 
obtained.  It  is  important  to  note  that  employing  this  value  for 
Too  gave  lower  values  for  the  velocity  constants  than  would  have  been 
obtained  by  taking  for  T«>  the  titration  value  at  equilibrium.  Al- 
though the  velocity  constants  show  a  greater  variation  in  value 
(due  to  the  influence  of  the  reverse  raction)  as  the  reaction  approaches 
equilibrium,  than  is  apparent  when  the  final  titration  value  for  7\o  is 
taken  for  calculating  the  results,  the  values  of  the  velocity  constants 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 


11 


at  the  beginning  of  the  reaction  are  more  consistent.  For  the  above 
reason  the  values  for  k\"  will  be  lower  than  other  values  given  in  the 
literature.  In  Table  II  the  results  of  an  average  experiment,  calcu- 
lated by  the  above  method,  are  compared  with  the  results  obtained 
by  using  the  titer  value  for  TM .  Too  =  calculated  value,  and  T'*>  = 
titer  value.  • 


TABLE  II 


Temp.  =  25°c. 


0.15  M.  HC1 


Too-r0=97.52 

r'oo-  To  =94.55 

Time 

T^-T 

(V  F.)  -  10* 

T^-T 

(ki*  Fe)  •  104 

Minutes 

157 

84.52 

9.112 

81.55 

9.402 

281 

75.49 

9.112 

72.52 

9.440 

421 

66.27 

9.176 

63.30 

9.526 

526 

60.39 

9.110 

57.42 

9.480 

736 

49.92 

9.098 

46.95 

9.502 

1148 

34.55 

9.039 

31.58 

9.552 

1455 

26.57 

8.934 

23.60 

9.536 

1829 

19.42 

8.823 

16.45 

9.560 

2091 

15.77 

8.713 

12.80 

9.562 

2966 

8.59 

8.190 

5.62 

9.519 

The  velocity  constants  for  the  different  acid  concentrations  are 
given  in  Table  III.  They  are  the  mean  of  the  constants  for  the  first 
half  of  the  reaction  which  in  all  cases  gave  concordant  results.  The 
constants  for  two  series,  differing  in  the  concentration  of  the  ester 
employed,  are  given.  In  each  series  two  determinations  of  the 
velocity  constants  for  each  acid  concentration  were  made  and  the 
mean  value  recorded.  ki'Fe  is  the  mean  velocity  constant,  Ci  is  the 
molal  concentration  of  hydrochloric  acid,  and  C%  is  the  normal 
concentration  of  hydrochloric  acid. 

(e)    CALCULATIONS  OF  THE  EQUILIBRIUM  CONSTANT 

In  the  calculation  of  the  velocity  constant  by  the  general  equa- 
tion, it  is  necessary  to  employ  a  value  for  the  equilibrium  constant. 
The  classic  work  of  Berthelot  and  St.  Gilles  gives  the  value  of  4. 
Knoblauch,  (Zeit.  physik.  Chem.,  22,  268  [1897])  using  an  equi- 
molecular  mixture  of  alcohol  and  water,  a  high  concentration  of  ester, 
and  hydrochloric  acid  as  a  catalyst,  obtained  2.67.  Jones  and 


12 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 


0.01 
0.03 
0.05 
0.07 
0.10 
0.15 
0.20 
0.30 
0.50 
0.70 
1.00 
1.50 


0.01 
0.03 
0.05 
0.07 
0.10 
0.15 
0.20 
0.30 


C2 

0.00952 

0.02857 

0.04759 

0.06666 

0.09510 

0.1425 

0.1900 

0.2840 

0.4726 

0.6604 

0.9354 

0.1391 


0.00987 

0.02961 

0.0493 

0.0690 

0.0985 

0.1477 

0.1966 

0.2944 


TABLE 

III 

0.470  N. 

Ester 

(fc'FeHO6 

(*i'Fe)-10» 

Ci 

6.11 

611 

18.30 

610 

30.00 

600 

41.79 

597 

60.15 

601 

91.10 

607 

122.2 

611 

185.5 

618 

312.4 

625 

45t).0 

643 

640.0 

640 

1006. 

671 

0.100  N 

.  Ester 

6.37 

637 

18.96 

632 

31.74 

634 

44.44 

635 

63.56 

636 

95.54 

637 

129.0 

645 

197.2 

657 

c, 

642 
641 
630 
627 
632 
639 
643 
653 
661 
681 
684 
723 


645 
640 
644 
644 
645 
647 
656 
670 


Lapworth  (Trans.  Chem.  Soc.,  99,  1427  [1911])  found  that  in  the 
presence  of  large  quantities  of  hydrochloric  acid  the  equilibrium  con- 
stant was  somewhat  greater  than  4.  With  methyl  acetate,  at  a  con- 
centration of  1.15  to  1.74  normal,  Griffith  and  Lewis  (Jour.  Chem. 
Soc.  109,  67  [1916])  obtained  for  K,  in  the  presence  of  N/2  hydro- 
chloric acid,  4 . 30,  4 . 52,  4 . 66,  and  4 . 80.  Since  no  definite  information 
regarding  the  value  of  K  for  the  hydrolysis  of  ethyl  acetate  in  the 
presence  of  hydrochloric  acid  of  concentrations  here  employed 
could  be  obtained,  the  equilibrium  constant  was  determined  at 
each  acid  concentration.  Great  accuracy  could  not  be  obtained 
on  account  of  the  experimental  conditions.  The  large  concentration  of 
water  forces  the  reaction  to  within  3%  of  completion,  thus  mag- 
nifying the  errors  of  the  determination.  However,  when  the  results 
in  Table  IV  are  compared  with  those  of  Griffith  and  Lewis  who 
employed  an  ester  concentration  four  times  greater  than  that  em- 
ployed in  this  investigation,  the  concordance  of  values  must  be 
considered  excellent,  and  a  good  confirmation  of  the  accuracy  of 
this  work. 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS  13 


K  = 


TABLE  IV 
(A-x)(B-x) 


Ci  A  X                          B  K 

0.01  0.4737  0.4600  52.85  3.39 

0.03  0.4737  0.4582  52.85  3.87 

0.05  0.4737  0.4596  52.85  3.50 

0.07  0.4737  0.4581  52.85  3.89 

0.10  0.4731  0.4576  52.79  3.87 

0.15  0.4728  0.4583  52.74  3.61 

0.20  0.4727  0.4567  52.73  4.01 

0.30  0.4713  0.4554  52.63  4.00 

0.50  0.4701  0.4545  52.45  3.93 

0.70  0.4679  0.4533  52.20  3.68 

1.00  0.4652  0.4519  51.91  3.35 

Mean  3.74 

Since  there  is  no  apparent  increase  or  decrease  of  the  equilibrium 
constant  within  the  limits  of  these  hydrochloric  acid  concentrations, 
and  since  the  mean  value  checks,  within  the  present  experimental  er- 
ror, the  value  of  Berthelot  and  St.  Gilles,  the  value  of  4  for  the 
equilibrium  constant  has  been  employed  in  all  subsequent  calcula- 
tions. 

(f)    METHOD     OF     CALCULATION,    AND    TABLES     OF    VELOCITY 
CONSTANTS  OF  HYDROLYSIS  COMPUTED  FROM  THE 
GENERAL  EQUATION 

Substituting  the  value  of  4  for  K  in  equation  (21),  the  final 
form  for  the  general  kinetic  equation  is 

..(22) 


t         n  —  6x 

In  order  to  employ  this  equation  it  is  necessary  to  obtain  the 
values  of  A,  the  initial  concentration  of  ester;  B,  the  initial  concentra- 
tion of  water;  and  x,  the  concentration  of  the  ester  changed  in  a  time 
t.  A  and  B  were  readily  obtained  since  the  weight  of  the  ester  and 
water,  and  the  density  of  the  solutions  were  known.  Their  calculation 
needs  no  explanation.  Therefore,  it  remains  only  to  show  how  x  is 
calculated  and  how  a  slight  change  is  made  in  To  and  in  the  first 
reading  of  /.  From  equation  (22)  when  t  equals  0,  x  must  equal  zero. 
Under  the  experimental  conditions,  it  is  impossible  to  start  the 
experiment  at  the  beginning  of  the  hydrolysis.  When  the  first  titra- 


14 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 


tion  is  made,  some  ester  has  hydrolyzed,  and  x  therefore  has  an 
appreciable  value  when  /  equals  0.  Therefore  TQ,  the  initial  titration, 
is  corrected  to  a  value  which  will  give  x  equal  0,  and  /  is  corrected  so 
as  to  make  the  beginning  of  the  time  the  moment  when  x  equals  °. 
The  following  consideration  will  explain  how  this  correction  is  made: 
Let  the  initial  titration  be  TQ.  Calculate  7\o.  Then  the  ester  equiva- 
lent, Te,  of  the  contents  of  one  pipette  of  the  solution  in  terms  of 
cubic  centimeters  of  alkali  is  calculated.  Then  T«>  -  Te  =  T'Q.  T'Q  is 
less  than  T0  by  a  quantity  of  alkali  equivalent  to  the  acetic  acid 
formed  from  the  beginning  of  hydrolysis  up  to  the  time  of  the  first 
titration.  Now  the  lapse  of  time  from  the  beginning  of  hydrolysis 
up  to  the  time  of  the  first  titration  may  be  computed  from  the  equa- 
tion: 


(23) 


This  time  is  added  to  the  time  period  of  each  successive  titration. 

rp <TV 

The  value  of  x  for  each  titration  will  be -•  A  =  x.    Table  V  gives 

a  comparison  of  the  velocity  constant  as  obtained  from  the  first 
order  and  second  order  equations. 


TABLE  V 


Ci=0.20 


02= 0.1897 


Equation  (9) 

Equation  (22) 

(1)              (2) 

(3) 

(4) 

(5) 

(6) 

(7) 

Time         T-T0 

(ki'Fe) 

Time 

r-7Y 

z(mols) 

(^l'Fe)'lO5 

Minutes 

Minutes 

48 

6.03 

0.02675 

71             8.47 

0.001240 

119 

14.50 

0.06433 

2.340 

158           17.82 

0.001236 

206 

23.85 

0.1058 

2.345 

259           27.48 

0.001234 

307 

33.51 

0.1486 

2.345 

371           36.71 

0.001226 

419 

42.74 

0.1895 

2.337 

491            45.42 

0.001226 

539 

51.45 

0.2283 

2.347 

638           54.30 

0.001218 

686 

60.33 

0.2676 

2.335 

837           63.90 

0.001208 

885 

69.93 

0.3102 

2.338 

1010           70.75 

0.001206 

1058 

76.78 

0.3406 

2.353 

97.00* 

103.  03r 

0.4570*' 

100.  45J 

106.48V 

0.4724  A 

i=end  point 

r=end  point 

x'  =  equilibrium  value  of 

x. 

j=T00-T0 

v  =  T00-r0=Te 

A  =  initial  cone,  of  ester. 

ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 


15 


From  the  Table  it  is  seen  that  the  time  of  hydrolysis  began  48 
minutes  before  the  first  titration  was  made,  and  in  that  time  enough 
acetic  acid  was  formed  to  neutralize  6.03  cc.  of  alkali.  The  time  in 
column  (4)  was  obtained  by  adding  48  to  the  figures  in  column  (1), 
and  the  values  in  column  (5)  were  obtained  by  adding  6.03  to  the 
figures  in  column  (2). 

Equation  (22)  gave  constant  values  for  k\"  when  calculated  from 
the  titrations  near  the  equilibrium  point  of  the  reaction.  In  Table 
VI  is  compiled  the  mean  values  of  ki"  obtained  by  equation  (22). 
d  is  molal  concentration,  and  c2  is  normal  concentration  of  the 
hydrochloric  acid.  (ki'Fe)  equals  k\' . 

TABLE  VI 

OA7  N.  Ester 


Ci 

0.01 
0.03 
0.05 
0.07 
0.10 
0.15 
0.20 
0.30 
0.50 
0.70 
1.00 
1.50 


0.01 
0.03 
0.05 
0.07 
0.10 
0.15 
0.20 
0.30 


0.00952 

0.02857 

0.04759 

0.06666 

0.0951 

0.1425 

0.1900 

0.2840 

0.4726 

0.6604 

0.9354 

1.391 


0.00987 

0.02961 

0.0493 

0.0690 

0.0985 

0.1477 

0.19660 

0.2944 


Ci 

1.167 

116.7 

3.442 

114.7 

5.729 

114.5 

7.971 

113.9 

11.46 

114.6 

17.36 

115.8 

23.27 

116.3 

35.34 

117.8 

60.05 

120.1 

86.03 

122.9 

125.2 

125.2 

196.1 

130.8 

0.100  N.  Ester 

1.166 

116.6 

3.450 

115.0 

5.782 

115.6 

8.094 

115.6 

11.55 

115..5 

17.57 

117.1 

23.65 

118.3 

35.95 

119.8 

122.6 
120.5 
120.4 
119.6 
120.5 
121.8 
122.5 
124.5 
127.1 
127.3 
133.8 
141.0 


118.2 
116.5 
117:3 
117.3 
117.3 
119.0 
120.3 
122.1 


Table  VI  shows  that  in  the  first  series  corresponding  to  an  initial 
ester  concentration  of  0.47  normal  the  values  obtained  for  the 
ratios  of  the  velocity  constants  to  the  hydrochloric  acid  normalities 
are  greater  than  they  are  in  the  second  series,  corresponding  to  an 
initial  ester  concentration  of  0.100  normal.  If  the  activity  of  the 
hydrogen  ion  is  not  changed  by  increasing  the  ester  concentration 


16  ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 

and  there  is  no  other  catalytic  influence,  then  according  to  the 
general  kinetic  equation  a  change  in  ester  concentration  at  constant 
hydrochloric  acid  normality  should  not  affect  the  velocity  constant. 
However,  this  difference  is  in  agreement  with  the  results  of  Griffith 
and  Lewis  (Jour.  Chem.  Soc.  109,  67  [1916])  who,  working  at 
constant  volume  and  at  constant  hydrochloric  acid  concentration, 
found  that  the  velocity  constant  increased  with  increasing  ester 
concentration.  They  ascribed  the  cause  to  a  negative  catalytic 
effect  of  the  water. 

II.  DISCUSSION 

The  hydrolysis  of  a  comparatively  simple  substance  as  ethyl 
acetate  may  be  regarded  as  a  type  reaction  for  all  hydrolytic  reac- 
tions. Consequently,  a  solution  of  the  kinetics  and  mechanism  of  this 
reaction  is  a  problem  of  very  great  importance.  However,  the 
phenomenon  of  the  simplest  case  of  hydrolysis  is  extremely  complex 
because  so  many,  ionic  and  molecular  species  are  involved.  To 
obtain  a  complete  solution  of  its  kinetics  requires  a  knowledge  of  the 
concentrations  and  activities  of  all  the  species  at  any  time  during 
the  course  of  the  reaction. 

The  position  which  is  taken  in  this  investigation  is  based  on 
thermodynamic  reasoning,  and  ascribes  all  the  catalytic  effect  of  the 
acid  to  the  hydrogen  ion.  An  inspection  of  Tables  I,  III,  and  VI 
show  that  in  each  case  the  ratio  of  the  velocity  constant  to  the 
concentration  of  the  hydrochloric  acid  gives  a  minimum  value 
somewhere  between  0.05  and  0.10  normal  concentration  of  hydro- 
chloric acid.  There  can  be  no  possible  doubt  that  this  minimum 
exists,  since  besides  being  supported  by  the  work  of  others  it  was 
verified  in  every  instance  in  the  present  investigation.  The  theory 
of  catalytic  activity  of  undissociated  hydrochloric  acid  molecules 
fails  to  explain  this  minimum. 

As  mentioned  in  the  introduction,  if  it  be  assumed  that  the 
potassium  ion  has  the  same  activity  as  the  chlorine  ion  in  a  solution 
of  given  strength  of  potassium  chloride,  and  if  it  also  be  assumed 
that  in  solutions  of  the  same  strength  of  hydrochloric  acid  and 
potassium  chloride,  the  chlorine  ion  activity  is  the  same,  then  it 
follows  that  the  hydrogen  ion  activity  coefficient  passes  through  a 
minimum  in  the  neighborhood  of  from  0.1  to  0.2  molal  concentration 
of  hydrochloric  acid,  and  then  rises  rapidly.  Employing  these 
assumptions,  which  have  considerable  evidence  for  their  support, 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 


17 


1.3 


12. 


I.I 


10 


00 

k.'Fc-rb6 


I2C 


18 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 


Harned  (loc.  cit.)  has  computed  the  independent  hydrogen  activity  in 
hydrochloric  acid  solutions  from  the  electromotive  force  data  of 
Ellis  (Jour.  Amer.  Chem.  Soc.  38,  737  [1916])  and  Noyes  and  Mac 
Innes  (ibid.  42,  239  [1920]).  The  hydrogen  ion  activity  coefficient 
from  these  results  is  given  by 

log  FH  =  0.330  c-0.  284  c0471 

(Harned—  Jour.  Amer.  Chem.  Soc.  44,  252  [1922]),  where  FH  is 
activity  coefficient  of  the  hydrogen  ion. 

ki'F 

In  Fig.  I  are  given  plots  of  -  e  (Table  VI)  against  log  GI  and  also 

c\ 

FH  against  log  c\.  It  is  clear  that  with  increasing  acid  concentration 
the  value  of  the  ordinate  first  passes  through  a  minimum  and  then  rises 
rapidly  in  both  cases.  The  minimum  of  each  curve  occurs  between 
0.07  and  0.20  molal  concentration  of  hydrochloric  acid.  However, 


in  dilute  solutions  F 


decreases  more  rapidly  than  —  —  e,   while  in 

c\ 


concentrated  solutions  it  increases  more  rapidly.  Therefore  if  the 
values  of  k\Fe  are  divided  by  the  activity  of  the  hydrogen  ion  a  con- 
stant is  not  obtained.  This  is  illustrated  in  Table  VII.  In  column 


(1) 

Cl 

0.01 
0.03 
0.05 
0.07 
0.10 
0.15 
0.20 
0.30 
0.50 
0.70 
1.00 
1.50 


(2) 


0.935 
0.903 
0.886 
0.875 
0.868 
0.858 
0.857 
0.867 
0.914 
0.979 
1.112 
1.416 


TABLE  VII 
(3) 

«.* 


0.997 
0.995 
0.993 
0.990 
0.983 
0.975 
0.964 
0.942 


(4) 
-HO6 


1.248 
1.270 
1.292 
1.302 
1.320 
1.350 
1.357 
1.359 
1.314 
1.255 
1.126 
0.924 


(5) 

k'Fe)' 
an.aw 
1.248 
1.270 
1.293 
1.303 


324 
357 
367 
373 
337 
287 
168 


0.980 


"Calculated  from  the  vapor  pressure  of  water  over  hydrochloric  acid  solutions 
(Harned — loc.  cit.) 

(1)  are  molal  concentrations  of  hydrochloric  acid,  and  in  column  (2) 
are  the  corresponding  activity  coefficients  of  the  hydrogen  ion; 
column  (3)  contains  the  activity  of  the  water  molecule  for  the 


ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS  19 

various  acid  concentrations;  Column  (4)  gives  the  ratios  of  the 
velocity  constants  (computed  from  the  general  kinetic  equation, 
Table  VI)  to  the  corresponding  hydrogen  ion  activities;  and  column 
(5)  contains  the  ratios  of  the  velocity  constant  to  the  product  of  the 
hydrogen  ion  and  water  activities. 

It  is  seen  from  the  Table  that  the  values  of  ^-^  and  ^ll^.  are 

aH  aB  -  aw 

not  constant,  but  have  a  maximum  at  0.3  M.  acid  concentration. 
This  is  not  due  to  experimental  error.  In  the  more  con- 
centrated solutions,  it  is  possible  that  the  deviation  is  due 
to  an  error  in  calculating  the  hydrogen  ion  activity  which 
may  have  a  lower  value  than  the  calculated  one.  On  the  other 

(ki'F } 
hand,  as  already  pointed  out,  — — -  should  not  be  a  constant  if 

<ZH  •  ow 

Fe  varies  with  the  acid  concentration.  The  value  of  Fe  in  solutions 
of  hydrochloric  acid  can  be  obtained  theoretically  from  either  the 
measurement  of  the  partial  vapor  of  the  ester  above  the  solution,  or 

k  fF 

from  the  solubility.    It  was  shown  that  ~ — -  s  should  be  constant. 

0H-aw 

Consequently,  if  the  solubility  decreases  with  increasing  acid  con- 
centration the  correction  for  Fe  will  be  in  the  right  direction.  A 
determination  of  the  solubility  is  difficult,  due  to  hydrolysis  taking 
place  in  the  presence  of  the  acid.  However,  a  number  of  determina- 
tions of  the  solubility  showed  that  the  solubility  does  decrease  as  the 
acid  concentration  increases  up  to  a  concentration  of  0.3  M.  and  this 

decrease  is  of  the  same  order  of  magnitude  as  the  increase  in  — — -, 

0H  '0w 

Another  factor  to  be  considered  is  the  possibility  of  a  change  in  the 
hydrogen  ion  activity  of  the  acid  caused  by  the  presence  of  the  ester. 
An  attempt  was  made  by  the  electromotive  force  method  to  deter- 
mine this  change,  but  owing  to  difficulties  caused  by  complex  liquid 
junction  potentials,  little  reliance  can  be  placed  on  the  results,  and 
further  work  must  be  done  before  any  conclusions  may  be  drawn. 

In  conclusion  it  is  thought  that  the  minimum  in  the  velocity 
constant — log  c  plot  is  contributory  evidence  of  the  theory  of  the 
independent  activity  coefficients  as  developed  by  Mac  Innes  and 
Harned.  On  the  other  hand  it  is  thought  that  further  evidence 
has  been  obtained  for  the  activity  theory  of  homogeneous  catalysis, 
and  that  work  of  this  nature  is  in  the  right  direction. 


20  ION  ACTIVITY  IN  HOMOGENEOUS  CATALYSIS 

SUMMARY 

(1)  The  general  theory  of  hydrolysis  of  ethyl  acetate  has  been 
considered,  and  the  activity  theory  has  been  applied. 

(2)  The  monomolecular  velocity  constants  of  hydrolysis  of  ethyl 
acetate   at   different   hydrochloric   acid   concentrations   have   been 
accurately  determined  at  25°  C.     Many  determinations  were  made 
with  acid  concentrations  in  the  neighborhood  of  0.1  M  hydrochloric 
acid. 

(3)  A  solution  of  the  general  equation  for  the  velocity  constant 
of  hydrolysis  has  been  obtained. 

(4)  The  velocity  constants  have  been  computed  by  the  general 
equation. 

(5)  In  four  series  of  measurements,  it  has  been  found  that  the 
plot  of  the  velocity  constants  divided  by  the  molal  concentration  of 
the  acid  against  log  c\   (ci  =  molal  concentration  of  hydrochloric 
acid)  shows  a  minimum  at  0.07  to  0.08  M.  concentration  of  the  acid. 
This  is  similar  to  the  plot  of  the  individual  hydrogen  ion  activity 
coefficient  against  log  c\  which  has  a  minimum  at  0.18  M.  acid 
concentration. 

(6)  It  has  been  shown  that  the  velocity  constant  divided  by  the 
product  of  the  activities  of  the  hydrogen  ion  and  water  molecule 
does  not  give  a  constant,  but  has  a  maximum  at  0.20  to  0.30  molal 
concentration  of  hydrochloric  acid. 

(7)  A  suggestion  is  made  that  the  deviation  from  constancy  is  due 
to  one  or  more  of  the  following  factors: 

(a)  That  the  activity  coefficient  Fe  of  the  ester  varies  with  a 
variation  in  the  acid  content  of  the  solution. 

(b)  That  the  activity  of  the  hydrogen  ion  is  influenced  by  the 
presence  of  the  ester. 

(c)  That  in  the  more  concentrated  solutions  of  hydrochloric  acid 
the  values  given  to  the  activity  coefficient  of  the  hydrogen  ion  may 
be  in  error. 

(8)  The  kinetics  of  hydrolysis  of  ethyl  acetate  is  very  complex, 
but  it  is  thought  evidence  has  been  obtained  to  show  that  the  method 
here  employed  is  in  a  general  way  correct. 


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19JO 


50m-7,'29 


Gay  lord  Bros. 

Makers 

Syracuse,  N.  V. 
PAT.  JAN.  21,1908 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


